Ramsey number $R(3,13)$

The smallest number $n$ such that any two-coloring of the edges of the complete graph $K_n$ must contain either a monochromatic $K_{3}$ in the first color or a monochromatic $K_{13}$ in the second color.

Updates

• 2013 Upper bound: $68$
  J. Goedgebeur and S.P. Radziszowski, New Computational Upper Bounds for Ramsey Numbers R(3, k), Electronic Journal of Combinatorics, http://www.combinatorics.org, #P30, 20(1) (2013), 28 pages.
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]
• 2015 Lower bound: $60$
  M. Kolodyazhny, Novye Nizhnie Granitsy Chisel Ramseya R(3, 12) i R(3, 13) (in Russian), Matematicheskoye i Informacionnoe Modelirovanie, Tyumen, 14 (2015) 126-130.
  [via Small Ramsey Numbers, Stanisław Radziszowski, 2024-09-06]